So I'm feeling a bit defensive as a colonial expat- the British view of Australian racism is, I think, a distortion and reading a British mentality into Australian culture. This is, I think, because in Britain you largely do not have alienated cultures that haven't adapted to post industrialised society. The closest you would get (from what I've seen) are the West Indian populations that struggle with familial dysfunction (disproportionately high divorce rate/single mothers, etc).
The aboriginal culture is so devastated by alcohol, that when the alcohol laws forbidding aboriginals to drink were repealed in the 70s it destroyed them. This was done because it was felt to be paternalistic and racist to forbid aboriginies to drink, and I certainly understand that view. But the fact of the matter is, aboriginals are, per capita, the highest funded group by government in Australia, by a long, long margin. At the end of the day, it's not that Australians don't care about, or don't want to do anything about aboriginal depravation or social problems, it's that unfortunately it isn't possible to modernize a culture from the outside.
There are many things that are part of traditional culture that are repugnant to most people, like the gifting of children to elders for sex as a token of respect. There was a report commissioned that was released in the early 2000's that detailed the extremely high levels of sexual abuse of children that was (in the words of the report) 'fuelled by rivers of grog'.
The view that Australians are racist is because I think that the British tend to think of racism in terms of 'othering' and about institutional barriers and ingrained attitudes that restrict others (like the class system). That doesn't exist in anything like the same way in Australia. In many socio-economic markers, non-aboriginals are almost all equally ranked in terms of life expectancy, health outcomes and incarceration rates. It's only aboriginal populations where these fall off the scale. Unfortunately it's not something that can be externally addressed. It is something that will have to come from within their own culture to respond (see the efforts of Noel Pearson for example).
To be explicitly clear, I am saying that aboriginal culture is fundamentally incompatible with modern society- traditional living in tribes on the land will never result in meeting the same socioeconomic markers that are expected from a modern society. Hospitals cannot be built and staffed in every remote location. Police and social services and teaching cannot be remotely staffed in every location. Tribal life is difficult, and extraordinarily foreign to almost any idea that you or I might have. Their concept of time is extremely fluid- everything is gauged roughly by the sun, so a European obsession with the time and punctuality doesn't fundamentally work. Concepts of ownership are very different. Aboriginal culture doesn't revolve around private property in the same way ours does, with a clear demarcation of private and public property. If you have something and others in the tribe want it, they will take it, because their view of ownership is tribal rather than individual.
European culture however does require (for instance) time keeping and private property- you won't be able to get and keep a job if you can't keep to time (Aussies are extremely intolerant of people slacking off at work- I've never met a people so hardworking with the exception of the kiwis). If you want aboriginies to meet European socioeconomic markers, then there needs to be a shift in their culture. This, combined with a genetic and cultural intolerance for alcohol leads to really terrible conditions, especially for women and children. Domestic and sexual violence is rife- something along the lines of 80% of children in tribes are the victim of sexual abuse. Part of this is alcohol issues, but part of it is that tribal culture doesn't see a problem with child sexual abuse.
There are some fundamentally incompatible elements of aboriginal tribal culture with modern society- no one wants to be racist, but do not imagine that Australians do not care, or that their society doesn't do what it can. But at the end of the day, you cannot force people to change cultural habits from the outside. When this report detailing child sexual abuse, domestic violence and alcohol and substance abuse was released, the government intervened and sent the military in to lock down those areas in an attempt to reign in some of the worst damage. It was viewed as inherently racist and eventually abandoned, but what else could be done? A quick Google reveals that aus gvt spending is around $20k per capita (of which around 30-40% is infrastructure spending & military). Indigenous expenditure in health and welfare alone is $17k per capita.
I'm aware this has become a very long post, so I'll cap it there, but I disagree that Australians are racist, or more so than average- migrant populations tend to do very well in Australia, and there is a very strong representation of non-white Anglo Saxon in virtually all walks of government and business. There is also a strong banter culture (it would be called in the UK) that people might take for racism, but is genuinely thought of as affection. If you aren't used to it, the Australian penchant for having a go at someone can be viewed as hostile when it's generally affectionate. Your worst enemy is 'a little bit of a bastard' but your best friend is 'a total bastard'. It's about understatement and hidden affectivity.